It's just after dawn and on the gleaming Pacific Ocean, 365 miles off the coast of Costa Rica, the hunt is on for pirates. But these 21st-century buccaneers are looting the treasure beneath the waves, not the gold and silver coins buried long ago on Cocos Island a few miles away.

Cocos, the remote emerald tip of a towering underwater mountain range which was the setting for the fictional Isla Nublar in the novel Jurassic Park, has served as a pirate hideaway, whaling station, penal colony and a pit stop for Colombian drug runners. It is the most shark-rich island on Earth and its underwater flanks serve as a nursery for myriad marine species, many unique.

The marine life around Cocos Island off Costa Rica is among the richest on Earth. Video: Alejandro Balaguer / Albatros Media

But these extraordinary riches are being plundered by illegal fishing, with many sharks, rays, turtles and mantas among the devastating collateral damage of longline tuna fishing. It is part of a global illegal fishing crisis worth $10-23bn a year that results in 100m sharks killed every year.

To combat the carnage, a new $1.5m radar system is being built - with backing from philanthropists including the actor Leonardo di Caprio - that will pinpoint pirate vessels up to 70 miles out. This will help enforce a new enlarged marine protection area that entered into force on 11 April.

The radar, the first of 13 in Costa Rica, will be followed by the first station and speedboat on Cocos of the national coastguard, which has greater legal powers.

Current efforts to counter the pirates are limited by resources and the size of the area that must be covered. On the 36-foot Cocos Island national park patrol boat, Captain Isaac Chinchilla points north-east into the steamy distance: “The fishing boats are usually there.”

After six miles of empty ocean, a grotesque sight bobs into view: eight feet of hacked-up, rotting whale carcass enmeshed in thick black netting, with one tail fin floating pink and raw. Attached is a wooden raft and a solar-powered radio buoy. The strange craft is designed to attract bait fish and is the first sign of piracy. “We are finding more and more of these,” says Chinchilla. “It is a new technique the pirates are using.”

A few miles on, a pale dot winks from the bright blue horizon. It is right on the cusp of the 12-mile limit within which fishing is totally forbidden. “If they have a longline attached, they will have seen us and cut it by now,” says Chinchilla. Soon another dot appears, then two more.

The patrol boat's engine roars and we race towards a fishing boat that has come into view and inside the forbidden zone. Half a mile off, the pirate vessel's chimney gives a great belch of dirty fumes and surges away. The pursuit is on, but the patrol boat runs it down: the capture is made precisely 56 yards inside the forbidden zone.

The pirate boat, Coopepes 20, is a rusting 60ft fishing vessel, its longline winch clear on the rear deck, alongside a barrel brimming with shining hooks. Its captain, bearded and with a thick silver chain on his bare chest, greets Chinchilla cautiously. Juan Carlos Barrantes tells Chinchilla he is low on fuel and drifted into the forbidden zone by accident. “So how did you run away so fast?” asks Chinchilla. “Well, I had a little left,” says Barrantes. It seems neither men believe the stories.

Barrantes tells the Guardian: “We don't agree with the no-take zone, though we have to respect it. But where else are we going to fish?” With a heavily tattooed crewmate, he tilts the barrel of hooks for inspection: “Look, the hooks are here. We are not fishing illegally.” Some of the hooks are J-shaped, outlawed since 2003.

Barrantes explains why he does not seek an easier way to make a living: “I have no education: I have to stay in fishing.”

Chinchilla issues a formal warning, his only power unless fishers are caught red-handed. But he adds that this encounter was a surprisingly pleasant one. Previously, the patrol boat has been rammed and Chinchilla and his crew routinely receive death threats.

Juan Carlos Barrantes on his fishing boat during checks by the Cocos Island patrol. Photograph: David Delgado / La Nación

Barrantes is now one of dozens of illegal fishermen caught in recent years, but only one has been convicted in a decade and they escaped a prison sentence. Every one of the 30 or so pirate vessels that loot the Cocos national park, a Unesco world heritage site, are well known to Chinchilla and his team. “It is hugely frustrating,” he says.

The undersea world at Cocos is as fantastical as the names of its inhabitants, from the sicklefin devil ray to the scarlet Mexican hogfish. Hammerhead sharks glide over a rocky floor studded with purple spiky urchins and cyan corals. Whitetip reef sharks laze ahead of their night-time feed, while mustard-yellow trumpetfish wriggle along past shoals of glittering bigeye jacks.

There are a minimum of 1,700 marine species found here, dozens existing nowhere else. A recent scientific study concluded Cocos was “one of the most extraordinary marine ecosystems on the planet”, particularly for the huge number of top predators. Nearly eight tonnes of fish inhabit each 100-metre square patch of coastline, far exceeding the Galapagos Islands which are part of the same chain.

But the illegal fishing lines, often 10km long, cause carnage. In the last two years alone, the park rangers have hauled in 364km of lines and 8,535 hooks, but this is likely to be a tiny proportion of the total set by fishermen. Shark finning, to serve Chinese diners, has also been a scourge.

It is hoped that the beefed up enforcement and new radar station will put a dent in that decline. But building it is no easy feat. The five-mile long island is also a haven for many unique land species – from the trumpet tree to the ruffed Cocos lizard – so every bag of cement and block is being carried on builders' backs up steep muddy paths to a fortified vantage point, 254m high.

“It is like the Egyptian pyramids – it is being built by hand,” says Zdenka Piskulich, at Costa Rica Forever, a national conservation fund. It is paying for the radar, along with CI and philanthropists group Oceans 5 which is backed by di Caprio. A small new hydroelectric dam, echoing one of the island's astonishing waterfalls, is also needed to provide power.

Piskulich, a lawyer, says there are legal obstacles to overcome too. Fishing boats must be forced to carry identification beacons and the current extremely high standard of evidence for prosecution must be adapted. That requirement for overwhelming proof comes from the high value placed on human rights by Costa Rica's legal system.

Cocos Island is the only peak of a huge underwater mountain range that breaks the surface. Photograph: Alonso Tenorio / La Nación

Another unusual feature of the country can hamper enforcement – it has had no armed forces since 1949. “Doing this in Costa Rica, which doesn't have an army or a navy, is very complex,” says Piskulich.

There is support from the US Coastguard, mainly a result of its war on the drugs traffic that runs through Costa Rica, but no military vessels can enter Costa Rican waters without the permission of all 57 senators every time.

David Delgado, security correspondent at Costa Rica's La Nación newspaper, says: “We are a peaceful people and I know this is good, but in this case there should be an exception. It's insane.” He says more enforcement bases and vessels are essential if the radar is to help in the fight against the pirates: “Right now they are in a war but without any barracks.”

Public security minister, Mario Zamora, acknowledges that while 25% of all of Costa Rica's land is already designated as national park, “it is only recently that we have looked to the oceans.”

Zamora, whose department controls the coastguard, says Costa Rica's laws are often unsuitable for crimes not committed on land. For example, he told the Guardian, suspects cannot be held for more than 24 hours without a court order but Cocos Island has no court and land is at least 40 hours away by boat, meaning suspects have time to dump incriminating evidence overboard.

“I regret not having taken the judges and district attorneys to the island for them to see how differently enforcement works at sea,” he says. “Until they walk in our shoes, they will not understand.”

CI director Quesada is clear that without change, Cocos could see an escalation of plundering: “The status quo is anything goes.”

He is angry at the looting of his country's natural wealth: “The people of Costa Rica take all the costs, while these illegal fishers are stealing all the profits.” The fishers get subsidised fuel, he notes, while enforcement vessels do not.

Furthermore, the income from rich recreational divers in Cocos makes each living shark worth $1.6m over its lifetime, according to recent analysis, while a dead hammerhead shark fetches just $195 in the port of Puntarenas. “But the country must also invest in education in coastal areas, as currently the people there have nothing else to do,” says Quesada.

Rafael Gutiérrez, executive director of Costa Rica's national conservation system which manages Cocos Island, says his organisation is working to provide alternatives to illegal fishing, such as farming red snapper and harvesting the Piangua clam from mangrove swamps, as well as supporting the development of whale– and dolphin-watching businesses.

Back on the patrol boat, having issued the legal warning to Barrantes and now towing the whale-baited fish attractor back to Cocos, Chinchilla reflects on the day. “It was positive, very good. But a really successful patrol would mean finding nothing at all.”